Quick P-Value question (2 tail vs 1 tail)

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birdec

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Question 27 on the morning CFAI Mock: A two-tailed t-test of the null hypothesis that the population mean differs from zero has a p-value of 0.0275. Using the significance level of 5%, the most appropriate conclusion is:
A. reject the null hypothesis
B. accept the null hypothesis
C. the chosen significance level is too high
The correct answer is A which is what I put because B says “accept” instead of “fail to reject” and C just looks wrong.
But, since it’s 2-tailed, I’m pretty sure it would be .0275*2 = .055, .055 > .05 level of significance so fail to reject null.
Any thoughts?
 
Nevermind, it must mean “the total p-value” rather than “the p-value under each tail”
 
I got A before looking at the answer. But from what I understood: 0.05 significance level is divided by 2 (b/c it’s a two tail test) = +/- 0.025.
And because the p value of 0.0275 is outside +0.025 (falls in the rejection region), we reject the null hypothesis..
 
birdec wrote:
Nevermind, it must mean “the total p-value” rather than “the p-value under each tail”
Click to expand...
No, there is no such thing as “total p-value”. When you calculate a p value you will get the same number regardles of whether it refers to a two-tailed or one-tailed test.
EDIT: This is the wrongest way I could possibly explain that, I apologize. The p-value is the probability that the null hypothesis lies beyond your calculated statistic. I was having the z-statistic in mind.
Tha alpha however needs to be adjusted for a one/two sided test. α = 0.05 for a one tailed test means that the 5% lies beyond the left or right point. For a two tailed test it means that 5% lies beyond both points, which is why you need to consider α/2 = 0.025 (since the distribution is symmetrical).
 
basically p shd b more than signifance level so we cant reject null right?
two tail and 1 tail hardly matters ???
 
ok so I divide alpha by 2 in a two-tailed test and compare it with the p-value that’s given. So in this case it would be a p-value of .0275 > .025 alpha so we fail to reject the null…? the p-value would be greater than the significance level. the correct answer is reject the null though.
 
This is very confusing. To the best of my knowledge, the correct answer is “fail to reject” in this case. It also is the case that we don’t “accept” the null so B has to be out of the question. I really don’t know what to advise here.
A p value gives you the probability that the hypothesized value falls outside of a region. That is why, after all, it is more difficult to reject for smaller α’s - they require smaller probabilities and they are difficult or more costly to obtain. (You might need an extremely large sample for example to get an adequately small standard error)
Let’s assume that this example was a z-test for simplicity :
A two-tailed 0.05 implies that, for the significance we are after , the standard deviations above which we can safely reject are 1.96
A p-value of .0275 implies that our value fell roughly within 1.92 deviations. This clearly is within the rejection area - we have to fail to reject.
I don’t know what else to say and I am in no position obviously to doubt official cfai material so let’s hope an expert statistician comes along?
 
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